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Aquifer Pump Test Theis Simulator

Compare time-drawdown curve, cone of depression, and Theis type curve to see how observation conditions affect estimates.

Parameters
Pumping rate Q
m³/day

Discharge from the pumping well.

Transmissivity T
m²/day

Ability of the aquifer to transmit water. Higher T gives a shallower, wider cone.

Storage coefficient S
-

Aquifer storage coefficient. Smaller S lets the effect spread faster and farther.

Observation distance r
m

Distance from the pumping well. Shown by the green vertical line.

Max pumping time
h

The animation pumps up to this elapsed time.

Elapsed time (scrub)
h

Scrub the elapsed pumping time back and forth.

Presets
Live results
—
Elapsed time t
—
Drawdown s at obs. well
—
Influence radius estimate
—
Theis u
—
Well function W(u)
—
Specific capacity Q/s
Cone of depression cross-section (deepening & widening over time)

Blue = water table; the funnel-shaped drawdown develops as pumping continues. The green vertical line marks the observation well at distance r, and the white dot shows its drawdown.

Time-drawdown curve (building up)
Theis type curve W(u) vs 1/u
Model and key equations

$s=\frac{Q}{4\pi T}\,W(u),\qquad u=\frac{r^2S}{4Tt}$

$W(u)=-\gamma-\ln u+\sum_{n=1}^{\infty}\frac{(-1)^{n+1}u^{n}}{n\cdot n!}=\int_{u}^{\infty}\frac{e^{-x}}{x}\,dx$

$s$ = drawdown [m], $Q$ = pumping rate, $T$ = transmissivity, $S$ = storage coefficient, $r$ = distance, $t$ = time, $\gamma\approx0.5772$ (Euler constant). $W(u)$ is the well function (exponential integral $E_1$). Smaller $u$ (longer time, closer distance) means larger drawdown. The influence radius is roughly $R\approx\sqrt{4Tt/S}$. The Theis solution assumes a homogeneous confined aquifer, radial flow, and a constant pumping rate; boundaries, leakage, unconfined storage, and well loss need other models.

How to read it

The time curve shows logarithmic drawdown growth with elapsed time.

The depression cone shows strong dependence on observation distance.

The type curve checks whether u is small enough for stable approximation.

Learn Aquifer Pump Test Theis by dialogue

🙋
When reading Aquifer Pump Test Theis, where should I look first? Moving Pumping rate Q changes both the plots and the result cards.
🎓
Start with Drawdown, but do not treat the number as the whole answer. Use Time-drawdown curve to confirm the assumed state, then read Cone of depression sketch for the distribution or trend. The time curve shows logarithmic drawdown growth with elapsed time.
🙋
I can see why Pumping rate Q changes Drawdown. How should I judge the influence of Transmissivity T?
🎓
Move Transmissivity T in small steps and watch Theis u. That reveals which term is controlling the result. Theis solution assumes a homogeneous confined aquifer, radial flow, and constant pumping rate. Boundaries, leakage, unconfined storage, and well loss need other models. A single operating point is not enough; sweep the realistic scatter range.
🙋
What is Theis type curve for? It feels like the ordinary curve already tells the story.
🎓
Theis type curve is for finding boundaries where the condition becomes risky or margin collapses quickly. The depression cone shows strong dependence on observation distance. In Initial interpretation of pumping-test data, the important question is often what happens after a small change, not only the nominal value.
🙋
So if Drawdown is within the target, can I accept the condition?
🎓
Treat this as a first-pass review. It helps with Planning observation-well distance and test duration and Sensitivity checks before transmissivity estimation, but final decisions still need standards, measured data, detailed analysis, and vendor limits. The type curve checks whether u is small enough for stable approximation.

Practical use

Initial interpretation of pumping-test data.

Planning observation-well distance and test duration.

Sensitivity checks before transmissivity estimation.

FAQ

Start with Drawdown and Theis u. Then use Time-drawdown curve to confirm the assumed state and Cone of depression sketch to read distribution or bias. The time curve shows logarithmic drawdown growth with elapsed time
Move Pumping rate Q alone, then move Transmissivity T by a comparable amount and compare the change in Drawdown. Theis type curve shows combinations where margin or performance changes quickly.
Use it for Initial interpretation of pumping-test data. Instead of trusting a single point, widen the input range and check whether Drawdown keeps enough margin before moving to detailed analysis.
Theis solution assumes a homogeneous confined aquifer, radial flow, and constant pumping rate. Boundaries, leakage, unconfined storage, and well loss need other models. Final decisions still require standards, measured data, detailed analysis, and vendor limits.

How to Use

  1. Enter pumping rate (Q) in m³/day—typical values 100–500 m³/day for municipal wells.
  2. Input transmissivity (T) in m²/day—sandstone aquifers typically 50–200 m²/day, fractured rock 5–50 m²/day.
  3. Specify storage coefficient (S)—unconfined aquifers 0.05–0.30, confined aquifers 0.0001–0.001.
  4. Set observation well distance (r) in meters from pumped well.
  5. Enter elapsed time (t) in hours from start of pumping.
  6. Outputs update automatically using the Theis equation s=Q/(4πT)·W(u): drawdown (m), dimensionless parameter u, influence radius, and specific capacity (m³/day/m). The tool performs the forward calculation only (no type-curve matching).

Worked Example

Municipal groundwater test: pumping rate Q = 250 m³/day from a confined sandstone aquifer with T = 120 m²/day and S = 0.0008. Observation well at r = 45 m after t = 4 hours (0.1667 day). The Theis dimensionless parameter u = r²S/(4Tt) = 2025×0.0008/(4×120×0.1667) ≈ 0.0203. Using the Cooper–Jacob approximation W(u) ≈ −0.577 − ln(u) ≈ 3.32, drawdown s = Q/(4πT)·W(u) ≈ 0.55 m. Influence radius √(4Tt/S) ≈ 316 m. Specific capacity = 250/0.55 ≈ 455 m³/day/m—acceptable for this well scenario. (The approximation requires small u; large storage values that give u≳1 fall outside its validity.)

Practical Notes

  1. Begin measurements 5–10 minutes after pump starts to capture early-time response and validate S estimates.
  2. Confined aquifers show slower drawdown than unconfined; verify S value against well logs and geological context.
  3. Distance-drawdown data from multiple observation wells refines T estimates; plot s versus log(r) to check linear behavior.
  4. Specific capacity below 100 m³/day/m suggests partial penetration, skin effects, or low-T conditions requiring screen analysis.
  5. Recovery test after pumping stops confirms S and detects non-ideal conditions (leakage, boundary effects).

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